Skip to main content
SpringerLink
Log in

Unification Modulo Associativity and Idempotency Is NP-complete

  • Conference paper
  • First Online:
Mathematical Foundations of Computer Science 2002 (MFCS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2420))

Abstract

We show that the unification problem for the theory of one associative and idempotent function symbol (AI-unification), i.e. solving word equations in free idempotent semigroups, is NP-complete.

Supported by the Ministry of Education of the Czech Republic under the project MSM 143100009.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baader F.: The Theory of Idempotent Semigroups is of Unification Type Zero, J. of Automated Reasoning 2 (1986) 283–286.

    Article  MATH  Google Scholar 

  2. Baader F., Schulz K. U.: Unification in the Union of Disjoint Equational Theories: Combining Decision Procedures, J. of Symbolic Computation 21 (1996) 211–243.

    Article  MATH  MathSciNet  Google Scholar 

  3. Baader F., Siekmann J. H.: Unification Theory, Handbook of Logic in Artificial Intelligence and Logic Programming (1993), Oxford University Press.

    Google Scholar 

  4. Baader F., Snyder W.: Unification Theory, Handbook of Automated Reasoning (2001), Elsevier Science Publishers.

    Google Scholar 

  5. Green J. A., Rees D.: On Semigroups in which xr = x, Proc. Camb. Phil. Soc. 48 (1952) 35–40.

    Article  MATH  MathSciNet  Google Scholar 

  6. Kapur D., Narendran P.: NP—completeness of the Set Unification and Matching Problems, In Proceedings of CADE’86, Vol. 230 of LNCS (1986) 489–495.

    Google Scholar 

  7. Kapur D., Narendran P.: Complexity of Unification Problems with Associative-commutative Operators, J. of Automated Reasoning 9, No. 2, (1992) 261–288.

    Article  MATH  MathSciNet  Google Scholar 

  8. Klíma O.: On the solvability of equations in semigroups with xr = x, Contributions to General Algebra 12, Proc. of 58th Workshop on General Algebra, Verlag Johannes Heyn, Klagenfurt 2000 (237–246).

    Google Scholar 

  9. Klíma O.: Unification Modulo Associativity and Idempotency is NP-complete, Technical report available at http://math.muni.cz/~klima.

  10. Klíma O., Srba J.: Matching Modulo Associativity and Idempotency is NP-complete, In Proceedings of MFCS’00, Vol. 1893 of LNCS (2000) 456–466.

    Google Scholar 

  11. Schmidt-Schauss M.: Unification under Associativity and Idempotence is of Type Nullary, J. of Automated Reasoning 2 (1986) 277–281.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mathematics, Masaryk University, Janáčkovo nám. 2a, 662 95, Brno, Czech Republic

    Ondřej Klíma

Authors
  1. Ondřej Klíma
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Informatics, Warsaw University, ul. Banacha 2, 02-097, Warszawa, Poland

    Krzysztof Diks  & Wojciech Rytter  & 

  2. Department of Computer Science, Liverpool University, Peach Street, Liverpool, L69 7ZF, UK

    Wojciech Rytter

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Klíma, O. (2002). Unification Modulo Associativity and Idempotency Is NP-complete. In: Diks, K., Rytter, W. (eds) Mathematical Foundations of Computer Science 2002. MFCS 2002. Lecture Notes in Computer Science, vol 2420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45687-2_35

Download citation

  • DOI: https://doi.org/10.1007/3-540-45687-2_35

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44040-6

  • Online ISBN: 978-3-540-45687-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation